A spherical metallic shell with 6 cm external radius weighs 6688 g. What is the thickness of the shell if the density of metal is 10.5 g per cm3?
(Take π = 22/7)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 2 cm
Concept
Volume = (Mass/Density)
If thickness is given then,
Volume of sphere = (4/3)π(R3 - r3)
Application
Volume = (6688/10.5)
According to the question
(6688/10.5) = (4/3) × (22/7) × (63 - r3)
(63 - r3) = (6688 × 3 × 7)/(22 × 4 × 10.5)
(63 - r3) = 152
216 - r3 = 152
r3 = 216 - 152
r3 = 64
r = 4
Now,
Thickness = R - r
= 6 - 4 = 2 cm